Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
229 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #87802 | C4 | semidirect |
| 13. C5×Dic20 | C4 | semidirect |
| 15. #87776 | C4 | semidirect |
| 42. C5×AGL(1,𝔽5) | Q16 | semidirect |
| 66. Dic20 | AGL(1,𝔽5) | direct (N × H) |
| 101. C52 | C4×Q16 | semidirect |
| 106. AGL(1,𝔽5) | Dic20 | direct (N × H) |
| 149. C5 | C4×Dic20 | semidirect |
| 150. C5 | Q16×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×Dic10 | 2 |
| D5×Dic20 | 2 |
| #11716837 | 2 |
| C5×C8×AGL(1,𝔽5) | 2 |
| #11716737 | 2 |
| Q16×AGL(1,𝔽5) | 5 |
| C4×Dic20 | 5 |